Books: Flatland

Flatland is a novella written by Edwin A. Abbot. It was first published in 1884, and rarely do social satire, fantasy, and higher-dimensional mathematics mix in such an eloquent fashion.

In Flatland, most of the characters reside in a two-dimensional world - they have length and width, but not depth. They move around like soap bubbles on a film, or like coins on a table. They are also geometric shapes (in an act of wry satire, the protagonist notes that social status is dependant on how many sides a shape has. The geometric shape of women? They are but lines, with only two sides.). All this is well and good until a resident of the third dimension arrives and whisks the protagonist off into the bizarre world of three dimensions. To say any more would be to spoil a clever and ultimately depressing story of not just higher dimensions, but human nature. Read it for yourself

Flatland is useful because we can reason into the fourth spatial dimension by analogy. 2D:3D as 3D:4D. Thus, a four-dimensional being would be able to see into our insides easily, just as we looking into Flatland would be able to see the organs of every Flatlander. No walls or cages could contain a 4D lifeform. As for us, we would only be able to see three-dimesional "slices" of the creature, just as a 2D being would only glimpse flat 2D sections of our body.